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problems-8-223-F07

problems-8-223-F07 - M ATH 223 Reading 2.10 3.13.3 P ROBLEM...

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M ATH 223 P ROBLEM S ET 8 D UE : 30 October 2007 Reading. § 2.10, §§ 3.1–3.3. Problems from the book: the starred problems may be carefully graded. You will be given a “completeness” score, depending on how carefully you complete these problems. • § 2.10: 1abc, 2, 3, 8, 9, 13, 16 • § 3.1: 1, 2, 8 , 9, 19 • § 3.2: 1, 4 , 5, 6 Additional problems: These will be carefully graded! 1. Let f : R 2 R 2 be defined by f ( x,y ) = ( x 2 - y 2 ,2xy ) . a. Show that f is one-to-one on the set A consisting of all ( x,y ) with x > 0 . [H INT : If f ( x,y ) = f ( a,b ) , then
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